Entwining structures, yang-baxter systems and duality theorems

Ziel

My research project is in very actively studied area of mathematics with connections to ring and module theory, Hopf algebras, non-commutative geometry and theoretical particle physics. The main directions of study will be the following:
a) We recently proved a new theorem connecting two concepts: entwining structures and Yang-Baxter systems. This important theorem will help us to give new examples of entwining structures and to classify them. This theorem will also provide new solutions for the Yang-Baxter systems.
b) We proved that the duality between the finite dimensional algebras and co algebras can be extended to a bigger category with a self-dual factor. We plan to study similar duality theorems for (co) rings, Lie (co) algebras, bialgebras, etc.
c) Unifying properties for the algebra and co algebra structures. We defined the Yang-Baxter modules, which unify the concepts of modules and co-modules. We will study their connections with the entwined modules and the (co) algebra Galois extensions. It also would be interesting to study the distributive laws in category theory and their connections with these concepts. We expect to present our results at the regular seminar devote to Algebra and Mathematical Physics, interact with the scientists from University of Wales, Swansea, obtain new results, and prepare the material for publication.. There will be collaborations with mathematicians from the USA, Romania, etc. We hope to make significant contributions to the work of the work leading experts in non- commutative gauge theory, Hopf algebras, braided categories, co homology theories, etc.

Wissenschaftliches Gebiet

Programm/Programme

FP5-HUMAN POTENTIAL - Programme for research, technological development and demonstration on "Improving the human research potential and the socio-economic knowledge base" (1998-2002)

Thema/Themen

Data not available

Aufforderung zur Vorschlagseinreichung

Data not available

Finanzierungsplan

RGI - Research grants (individual fellowships)

Koordinator

UNIVERSITY OF WALES SWANSEA

EU-Beitrag

Keine Daten

Adresse

Singleton Park
SA2 8PP SWANSEA
Vereinigtes Königreich

Gesamtkosten